Ashley,
what you have described is a common issue that people have with the Sims 3 game. I have done research since I am one of those who have suffered from this issue as well. My computer was well beyond the requirements. I had played the game for a few days and then my computer just suddenly shut down completely overheated.I have also played other games with higher requirements then this with very little or no issue (one game was a little laggy)
The reason I found after researching this issue is that the game "Sims 3" "When I finally got my Sims 3 installed and ready to go, I realized that it was pushing my ASUS GeForce GTX 580 DCUII, which is a card that runs incredibly cool, to the 70 Celsius range, with the fans at 70% speed. At first I thought it was the crazy summer heat, but I was wrong. Shocking, isn't it?
What was the issue? Well, this 2009 game was pushing my graphics card to render over 1,000 Frames Per Second (FPS). Logically, this exerts more strain on the GPU and thus more heat. I will explain the details of V-Sync and Overheating in my next post."
This link does go on to explain how to fix this. If this does not work fro you I encourage you to research further. THE GAME IS THE PROBLEM! Not the computer you have. EA games has even admitted to the issue on several sites. ( included this in the second link as well as a second possible option to fixing the issue.
I do however caution you to be careful in that continued overheated of the graphics card can fry your card and maybe even your computer's motherboard. So watch your temp while attempting to fix the issue.
http://www.thelonelycomputer.org/2012/06/fixed-sims-3-overheat.html#.Ud2_4fnCaSo
FPS Limiter and The Sims 3 | BeyondSims